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Enumeration of paths in Young--Fibonacci graph

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arxiv 2012.06379 v1 pith:LJNFALK2 submitted 2020-12-11 math.CO

Vsevolod Evtushevsky This is my paper · ORCID
classification math.CO
keywords graphyoung--fibonaccienumerationpathsalongdiagramdifferentialexplains
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The Young--Fibonacci graph is the Hasse diagram of one of the two (along with the Young lattice) 1-differential graded modular lattices. This explains the interest to path enumeration problems in this graph. We obtain a formula for the number of paths between two vertices of the Young--Fibonacci graph which is polynomial with respect to the minimum of their ranks.

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  1. Central measures on the r-differential version of the Young--Fibonacci graph

    math.FA 2024-11 conditional novelty 6.0 of 10

    For every r>=2, the Martin boundary of the r-differential Young-Fibonacci graph is described explicitly by boundary words with a parameter beta, plus the Plancherel measure, and all these measures are ergodic.

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